Sichen DuanJun Maoand Qian Zhang

（1.Institute of Materials Genome＆Big Data，School of Materials Science and Engineering，Harbin Institute of Technology，Shenzhen 518055，China；2.State Key Laboratory of Advanced Welding and Joining，Harbin Institute of Technology，Harbin 150001，China）

Abstract：One of the abundantly available energies that could be found in industrial power plants，running vehicles，nuclear power stations，etc.is known as thermal energy.A physical phenomenon known as thermoelectricity converts thermal energy into electrical energy and vice versa，providing a green route for power generation and a potential solution to the world energy crisis.The thermoelectric conversion efficiency is generally characterized by the temperature-dependent dimensionless figure of merit（zT），which is generally promoted by increasing the power factor and reducing the thermal conductivity.The present work reviews heat transmission in thermoelectric materials，particularly phonon engineering to reduce the lattice thermal conductivity.The two leading strategies of point defects engineering and nanostructuring for reducing thermal conductivity have been summarized.The optimized reported zTs of various thermoelectric materials in terms of reduced thermal conductivity have been presented.

Keywords：phonon transport；engineering defects；nanostructuring；thermal conductivity；zT；thermoelectrics

0 Introduction

Thermoelectric（TE）materials provide an alternative mechanism for power generation and solidstate cooling by converting thermal energy（waste heat）into electrical energy mutually and reversibly.The reserves of fossil fuels（gas，oil，and coal）are limited and would last up to 2042（gas and oil）and 2112（coal）［1］.According to the data published by the International Energy Agency，European Environmental Agency and Energy Information Administration，87% of energy in the world comes from burning fossil fuels［2］.Approximately 17% of energy out of 87% is used for useful work，and the remaining 70% is wasted in the form of heat［3－6］.With the passage of time，fossil fuels are gradually depleted and more energy is lost as heat.This has compelled researchers to focus on harnessing unused energy（wasted energy），which can bring sustainability as well as extend the depletion period of the reserves.

Fabrication of thermoelectric generators（TEGs）has become an area of attention in the field of energy harvesting for small and large sorts of applications，depending on size，materials used and power delivered.Thermoelectric generators are normally divided into two types，micro-TEGs and large bulk-TEGs［7－8］.Micro-TEGs can generate electrical power in the range of microwatts to milliwatts，while the bulk-TEGs can provide the output power from several to hundreds of watts.Thermoelectric generators are used in high，medium and low-power applications including aerospace，automobiles，industrial electronics，medical wearable，and wireless sensor network［9－12］.

The energy conversion efficiency of TEGs，also known as thermoelectric conversion efficiency，is expressed as［13－14］：

whereThandTcare the temperatures at the hot end and cold end，respectively.MzTis the thermoelectric figure of merit and can be expressed as：

whereTis the absolute temperature in Kelvin，κis total thermal conductivity，σis electrical conductivity，αis the Seebeck coefficient andα2σis the power factor.According to the different temperature ranges for practical applications，TE materials are broadly divided into three families.Typical TE materials and their operating temperature ranges are presented in Table 1［15－21］.

Table 1 Typical thermoelectric materials and their operating temperature ranges

zT≥3 is the target value of more advanced TE materials［22］.However，thezTvalues for TE materials reported previously are still lower than the target value.To improve thezTs，it is necessary to increase the numerator（α2σ）and decrease the denominator（κ）values in Eq.（2）.In Eq.（2），αandσcan be mathematically expressed as：

and

wherekBis the Boltzmann constant，his the plank constant，m*is the effective mass of the charge carrier，nis the charge carrier concentration，eis a charge on carrier，andτis the relaxation time.From the right-hand side of Eqs.（3）and（4），it is clear thatαandσare inverse parameters of each other with respect tonandm*.Therefore，this task is quite challenging to decouple these intertwined parameters and optimize the ultimateMzTvalues.In Eq.（2），κis the totality of the electronic part（κe）and phonon part（κl）.Therefore，Eq.（2）can be rewritten as：

where

and

whereLis the Lorenz number，vis the phonon velocity，Cis the specific heat capacity andlphis the phonons mean free path（MFP）.According to Eq.（6），κeis directly proportional toσ，which means highσvalues cause highκevalues.For instance，metals show high values of bothκeandσbecause the dominant part of heat conduction in metals is electrons.Generally，we use differentLfor metals and semiconductors，whereL＝2.44×10－8W·Ω／K2for most metals（degenerate limit）andL＝1.5×10－8W·Ω／K2for non-degenerate semiconductors［23］.Phonons（quantized lattice vibrations）are the leading carriers of heat in non-metallic crystalline materials.The quantum theory of lattice vibration and the phonon concept were established for understanding heat conduction in crystalline solids.The speed of propagation of acoustic phonons in the lattice is known as phonon velocity.The velocity of phonon is determined as the group velocity，which can be mathematically expressed asVgr＝?ω/?K［24］.ωis the frequency of the acoustic wave andKis the wave vector of the vibration associated with its wavelength byK＝2π/λ.At low values ofK，phonons with longer wavelengths can propagate for large distances in the lattice.However，this behavior fails at large values ofK.MFP of phonon is the average distance between the guest atoms.Thermal conductivity is contingent on how far phonons are portable between scattering events（their MFP）.In non-metallic materials，κresults from the collective contributions of phonons with wide-ranging MFP.Recently，the MFP of the phonon can be experimentally measured［25］.Fang et al.［26］theoretically calculatedκfor intrinsic and doped silicon carbide（SiC）.Because of the lownof the intrinsic semiconductor，κecan be ignored.However，for semiconductors with high doping concentration，κeof electrons cannot be ignored，and there thermal conductivity is mainly affected by phonon scattering of electrons and ionization impurity scattering.To be more specific，it is quite challenging to improve theMzTvalues due to the robust combination betweenα，σandκeasαis contrariwise ton，whereasσandκeare directly proportional ton.

It is clear thatκlcan be suppressed by reducing the MFP of the phonon.Geometrical effects，such as atomic-scale point defects，mesoscale grain boundaries，artificial induced nanoscale dislocations，nanostructuring，etc.，limit the MFP of phonons.In this article，we review some basic approaches using which phonons scattering can be enhanced and theMzTvalues are improved in TE materials.

1 Atomic-scale Point Defects Approach

1.1 Elemental Doping or Alloying Approach

This approach can be accomplished via elemental doping/alloying in the host compound.The thermal resistance of pristine compounds increases by introducing point defects in its crystals.Elemental doping/alloying introduces mass fluctuations and field strains in the matrix of the host compounds，which are caused by differences in their atomic masses and ionic sizes，respectively.

Theoretically，κlcan be calculated as follows［27－29］：

whereh，θDandΩare Planck’s constant，Debye temperature，and volume per atom，respectively.

In Eq.（9），vis the average sound velocity and can be expressed as：

wherevlandvtdenote longitudinal and shear sound velocities.

Γis the scattering parameter and contains three parts i.e.，mass difference，strain field and binding force difference.If the binding force difference is not taken into consideration，the scattering parameters of the mass difference（ΓM）and strain field（ΓS）can be written as［30］：

where

Among them，Miis the atomic weight of theith substitution atom，Mis the atomic weight of the original atom，δisubis the atomic radius of theith substitution atom，δis the atomic radius of the original atom andxiis the ratio of ith substitution atom.

In Eq.（14），εis a material-related parameter that is given by：

whereγis the Gruneisen parameter

Vp＝ris the Poisson ratio and can be expressed as：

Therefore，the total scattering parameterΓtotalis：

Enhancing phonons scattering by point defects requires large field strains and large mass fluctuations.However，due to the creation of perturbations in the periodic potential，particularly with large strains affecting the mobility（μ）of the charge carriers（Fig.1（a）），it is necessary to choose the doping/alloying element that has a smaller size difference from the host atom.In other words，to decoupleκlandμwith respect to point defects，it is necessary to choose the doping/alloying component that has a larger mass variance and almost similar ionic size compared with the host atom（Fig.1（b））.Liu［31］et al.proposed that inp-type（Nb，Ta）FeSb andn-type（Zr，Hf）NiSn alloys，lanthanide contraction paved the best way to suppressκlto the minimum while maintainingμunaffected，as shown in Fig.1（c）and（d）.For example，the atomic radii of Hf and Zr are nearly similar，i.e.208 pm and 206 pm，respectively，but there are large differences in atomic mass.Also，Nb and Ta have large differences in atomic mass，but possess nearly similar atomic radii，i.e.198 pm and 200 pm，respectively.The large difference in atomic masses and nearly similar atomic radii in the above mentioned alloys results in a large scattering of phonons and very less perturbation in periodicity of potential，respectively.

Fig.1 （a）More considerable radius difference between host atoms（blue and brown yellow）and alloyed atoms（red）generates more substantial perturbation to the periodic potential and thus deteriorates the charge carrier transport；（b）schematic depicts that weak effect on charge carrier transport can be realized if there are more minor radius differences between host atoms and alloying atoms；（c）and（d）displays the effects of Ta and Hf elements on κL and mobility μ of NbFeSb，and ZrNiSn，respectively.μo and κLo represent mobility and the lattice thermal conductivity for the pure compound，respectively.（Reproduced with permission［31］，Copyright ? 2018，John Wiley and Sons）

The use of various elements to introduce point defects in Bi2Te3-based TE materials has been reported，such as In，Cl，F(xiàn)e，Ag，Br，Cu，Sn and Ga［32－40］.An enhancement inMzTvalues was attributed to the reduction ofκland improvement of electronic transport properties.The reduction inκlwas due to the enhanced phonons scattering caused by point defects.AMzTvalue of～0.74 at 373 K was reported inn-type（Bi0.99Ag0.04）2（Te0.96Se0.04）3prepared by mechanical alloying（MA）and spark plasma sintering（SPS）［35］.κlwas reduced，while an opposite trend forα2σwas observed.Ag doping introduced point defects in the crystal structure and phonon scattering was enhanced.ImprovedMzTof～0.8 and～0.65 at 300 K were reported in 1 at% Cr intercalated and substituted Bi2Te3，respectively［37］.Cr either by substitution or intercalation resulted in point defects in the matrix，which scattered highfrequency phonons andκlwas reduced.At 300 K aMzT～1.09 was achieved in polycrystalline 1.0 at% Fedoped Bi0.48Sb1.52Te3［40］.Fe doping has been shown effective in enhancing theα2σdue to the optimization ofn.Also，κlwas suppressed by strong phonon scattering initiating from the atomic mass variance among Fe，Bi，and/or Sb.Lee et al.reported a highMzT～1.2 at 320 K in 0.5 at% In-doped Bi0.4Sb1.6Te3polycrystal［38］.As a result of the control amount of In or Ga doping，theκlwas suppressed by strong pointdefect phonon scattering.Nearly comparable power factors were observed in doped and undoped samples because of the resemblance of the density of states near the valence-band maximum.

In the 1950s，Ioffe proposed that forming solid solutions is an effective strategy for improving TE performance［41］.The compounds with the same crystalline and bonding nature can form a solid solution to suppressκl.For example，in Bi2Te3-Sb2Te3and PbTe-PbSe solid solutions，κlwas suppressed to 0.909 and 1.0 W/（m·K）from 2.0 and 1.538 W/（m·K），respectively.Korkosz et al.reported aMzTvalue of～2.0 at 800 K in the pseudoternary Na-doped（PbTe）0.86（PbSe）0.07（PbS）0.07［42］.They ascribed this highMzTto the very lowκl.The atomic mass variation and atomic size differences among the Te，Se and S elements introduced more point defects in the crystal structure of PbTe，hence the phonon scattering was enhanced.This approach has been extensively employed in inorganic TE materials including the metal-based chalcogenides［43－47］，half-Heusler（HH）compounds［48－54］，Zintl phase compounds［55－57］，selenides［58－59］，silicides［60－61］，etc.

Alloying of SnS witha similar crystal structure and bonding nature to SnSe leads to phonon scattering owing to atomic mass fluctuations and large dissimilarities in atomic radii between S and Se elements［62－63］.MzTof 0.64 and 1.0 at 823 K were obtained.κlwas decreased from～0.57 to～0.36 W/（m·K）and from 0.59 to 0.32 W/（m·K）at 823 K.Alloying strategy is also used to increase the bandgap and boost the inferior TE performance of materials.For example，Ag2Te material shows lowκand highμvalue，but theMzTvalue in its pristine form is only 0.6.The low performance of this material is because of the nearly intrinsic conduction due to the small bandgap.AMzTof～1.0 was realized by increasing the bandgap of Ag2Te when it is alloyed with PbTe［64］.The deleterious effects of minority carriers were reduced by increasing the bandgap，and the electronic transport properties were enhanced.Alloying in bulk materials also makes it conceivable to direct the convergence of several valleys.High valley degeneracy leads to a high effective mass and thenα.Ioffe et al.obtained a convergence of 12 valleys in Pb0.98Na0.02Te1－xSexalloys，which led to a highMzT～1.8 at 850 K［41］.

1.2 Vacancy Engineering Approach

The effect on TE properties of defects formed caused by introducing vacancies in the matrix are also notable［65－69］.Vacancies introduce missing atoms and missing interatomic linkages in the matrix and enhance phonon scattering.Asfandiyar et al.introduced artificial Sn vacancies in the SnS and SnSe-SnS samples，which broke translation symmetry and boosted phonon scattering［63］.Consequently，κwas suppressed compared with their pristine counterparts.All the vacancy-containing samples showed inferiorκlto the pure SnSe sample as depicted in Fig.2（a）.Sn vacancies introduced strong phonons scattering and as a result，κlwas suppressed.Also，charge carrier density increases by introducing vacancies in the matrix.In fact，introducing artificial vacancies resembles hole-doping in the matrix.Fermi level shifts into the valence band due to an upsurge in the hole concentration as shown in Fig.2（b）.For example，thenvalue of 0.6×1019cm－3in pure SnSe was increased to 1.07×1019cm－3upon introducing vacancies（Sn0.95Se）.zTsof～1.0 and～2.1 at elevated temperatures were reported in Sn0.985S0.25Se0.75and Sn0.95Se，respectively［63，65］.They attributed the highMzTto the lowκland enhancedα2σresulting from Sn vacancies.

Fig.2 （a）Lattice thermal conductivity of pure and vacancy-containing samples.Vacancy containing samples witnessed low κl values resulting from enhanced mid-frequency phonons scattering；（b）n of pure and vacancy-containing samples，confirming that n increased with the introduction of vacancies in the SnSe compound（（a）and（b）Reproduced with permission［65］，Copyright ? 2018，ACS publications）；（c）HAADF-STEM image of Eu2Zn0.98Sb2 and（d）κl of Eu2Zn1-xSb2（x=0，0.01，0.02，and 0.04）.The pinkfilled circles represent Eu atoms while the blue-filled circles represent Sb atoms（Reproduced with permission［67］，Copyright ? 2019，PANS）

Cu vacancies are easy to form in the CuAgSe and change from stoichiometric to non-stoichiometric compounds［68］.Cu vacancies significantly tunenand lead to high electrical conductivity in the CuAgSe.Also，Cu vacancies act as point defects，when scattered phonons andκwas simultaneously suppressed.High TE performance can be witnessed in the off-stoichiometric InSe-based thermoelectric materials［70－75］.The TE properties were tuned by deficiency of Se elements.The performance of Bi2O2Se was improved upon introducing Bi vacancies in the system［76］.Introducing Ag defects（Ag vacancies）in the Ag1－xGaTe2，the performance was improved approximately two times compared with its stoichiometric counterpart（AgGaTe2）［77］.

Zintl compounds are deliberated to be potential TE materials for use at the medium-ranging temperatures.Chen et al.prepared Eu2Zn1－xSb2bulks by high-energy ball milling and hot pressing［67］.This 2-1-2-type Zintl phase compound has a 50% intrinsic Zn vacancy，which induces an ultralowκl（see Fig.2（c）and 2（d））.Due to the smaller atomic number，Zn appeared darker，while Eu and Sb showed bright columns due to their more enormous atomic masses as shown in Fig.2（c）.It is obvious that half the sites in this crystal structure are occupied by Zn atoms（yellow filled circles）.In contrast，half sites are unoccupied（yellow open circles），which validates 50% intrinsic Zn vacancy.AMzT～0.6 at 700 K was achieved in the Eu2ZnSb2compound.With increasing extrinsic Zn vacancy，κlwas further reduced and the electrical properties were optimized，giving rise to an improvedMzT～1.0 at 823 K for Eu2Zn0.98Sb2.

2 Nanostructuring Approach

The TE performance of materials can be effectively manipulated by nanostructure engineering.This approach can lead to reduction inκl，which results from enhanced phonon scattering at the interfaces while also through quantum confinement effects for an increase inα.A particular nanostructure can effectively manipulate the TE performance of inorganic materials.Dimensionality can play a crucial role in reducingκl.For example，strong phonon scattering can be witnessed in low-dimensional materials due to a large number of interfaces compared with their bulk counterparts.In the following sections，a brief discussion has been made on one，two and three-dimensional nanostructure materials.

2.1 One Dimensional（1D）Nanostructure

The electronic density of states is concentrated at certain energies if the diameter of one-dimensional material such as nanotubes or nanowires is sufficiently small.Decreasing the diameter of nanowires to a few quantum states causes a split in energy bands，which leads to a decrease in theκlwithout affecting the electrical transport properties.To date，there are few research studies on the TE performance of 1D materials.

Harman method（resistance measurements by DC and AC methods）was used in obtaining theMzTvalues of isolated nanowires.Also，the suspended microchips technique was used to measure the TE properties［78］.Chen et al.reported aMzTvalue of～0.9 at 353 K for Bi2Te3nanowire arrays using the electrodeposition technique［79］.Also，it was reported that theMzTvalue might decrease with time due to oxidizing the nanowire surface.AMzT～0.82 was attained in Bi2Te3wire of size 200 nm［80］.A highMzTof～1.0 and～0.6 were reported in silicon 20 nm and 10 nm wide nanowires，respectively［81］.This value is 100 times higher compared with its bulk silicon counterpart（bulk siliconMzT～0.01 at 300 K）.The enhancement inMzTof these nanowires can be attributed to the reduction inκlwhen the diameters are small enough as shown in Fig.3.

Fig.3 （a）High-resolution image of 20 nm wide Si nanowires；（b）κ，presented as κbulk/κnanowire.The inset displays the area of the device containing the nanowires before（top）and after（bottom）the XeF2 etches to eradicate the nanowire.The yellow dashed frame represents nanowires.（Reproduced with permission［81］，Copyright ? 2008，Springer Nature）

2.2 Two Dimensional（2D）Nanostructure

In 1993，Kim and co-workers suggested thatMzTcould be optimized to its maximum values by forming thin films（quantum-well superlattices）of certain materials［75］.They calculatedMzTfor Bi2Te3thin films.The calculatedMzTwas 13 times higher than that of its bulk counterpart.This higherMzTin thin films was attributed to the reducedκlresulting from enhanced phonons scattering between layers.Venkatasubramanian et al.obtained aMzTof～2.0 at 300 K in Bi2Te3and Sb2Te3layered thin films［82］.The prepared films using organic chemical vapor deposition were c-oriented.In 2001，the aboveMzTwas further enhanced to～2.4 at the same measured temperature by optimizing the phonon scattering in the thin film［83］.

Besides，other two-dimensional materials，including PbTe/Pb0.93Eu0.07Te［73］，PbTe/PbSe0.2Te0.8［84］，and Si0.85Ge0.15［85］have been widely studied，and their performance has been improved.The enhancement inMzTof these films has generally been ascribed to the reducedκl.Lee and co-workers examined theκof Si/Ge superlattices with periods between 30 to 300?［85］.They found thatκof these superlattices is lower than that of Si/Ge alloys.With decreasing superlattices period（30＜L＜70?），a decreasing trend in the room-temperatureκalong the in-plane direction was experimentally observed.However，superlattices with comparatively long periods（L＞130?）show lowerκthan those of short-period samples.This unforeseen lowκin longer period samples was credited to the robust interruption of the lattice vibrations by prolonged defects formed throughout lattice-mismatched development.In 2000，the TE performance of Si/Ge superlattices was reinvestigated［86］.The results forκwere similar to those of Lee’s work，as depicted in Fig.4.Both results show an increasing trend inκwith increasing temperature.A similar tendency inκwas also observed in GeTe/Bi2Te3superlattices.Tong et al.have suggested two possible mechanisms for this abnormal result［87］.1）κis affected by thermal boundary resistance i.e.，the low-temperature thermal boundary resistance of samples becomes bigger and increases with increasing frequency and 2）considers the factor ofκein the partially coherent regime，which is based on the wave-particle duality of phonons.A single-element thin-film superlattice SiGe/Si coolers were prepared［88］.The two-fold improvement in the TE performance was accredited to the reducedκ.

Fig.4 （a）κ of Si/Ge superlattices.Each symbol is labeled by a superlattice period L measured in?；（b）κ of undoped Si/Ge superlattices.（Reproduced with permission［85-86］，Copyright ? 1997，AIP Publishing and Copyright ? 2000，Elsevier）

2.3 Three-Dimensional（3D）Nanostructure

Nanostructuring of 3D bulk materials leads to high density of grains，nanoscale precipitate secondary phases，lattice defects and distortions.κlcan be suppressed over a wide temperature range by strengthening all wavelength phonon scattering.Dresselhaus and coworkers have exposed that the bulk materials containing nanoparticle inclusions show better TE performance than those without nanoparticle inclusions［89］.

Bi2Te3bulk nanostructure was prepared by MA followed by SPS and their TE performance was studied.A highMzTvalue of～1.3 at 373 K was obtained for nanostructured bulk Bi0.5Sb1.5Te3sample［90］.Mehta et al.prepared nanostructured（BiSb）2（TeSe）3bulks samples using microwave technique and reported aMzTof～1.1［91］.AMzTof～1.16 at 420 K was reported in a nanostructured Bi2Te3bulk sample synthesized by a wet chemical method followed by SPS［92］.AMzTof～1.4 at 373 K was achieved in a nanostructured BixSb2－xTe3bulk sample prepared by high-energy ball milling and hot pressing［93］.Xie and co-workers subjected the Bi0.52Sb1.48Te3sample to annealing followed by SPS and enhanced theMzTto～1.56 at 300 K［94］.At 320 K a highestMzT～1.86 was reported in Bi0.5Sb1.5Te3compounds［95］.This enhancement inzTvalue was attributed to the lowκlresulting from enhanced midfrequency phonons scattering by nanoscale dislocation arrays，as depicted in Fig.5（a）.

Nanoscale precipitate secondary phases can be introduced by the formation of the solid solution to enhance TE performance.There are two kinds of precipitates（coherent and incoherent precipitates）formed in a solid solution matrix.The coherent nanoscale precipitates scatter long wavelength phonons.Unlike coherent precipitates，incoherent nanoscale precipitates have a large disparity with the matrix and scatter short wavelength phonons.Li et al.theoretically investigated phonon transport across coherent and incoherent interfaces［96］.The simulation results indicated that the phonon defect scattering becomes stronger with decreasing phonon wavelength.For phonons with shorter wavelength，they observed a strong phonon scattering across incoherent interfaces.Our previous work reported a highMzTvalue of～1.75 at 823 K for SnS-SnSe solid solutions［63］.This highMzTwas ascribed to the very low value ofκ.The existence of AgSnSe2nanoscale coherent precipitates within the grains contributes to an impressively lowκl.（Fig.5（b））.AMzTof～0.6 at 750 K was obtained in SnSe［97］.The lowκlwas due to the formation of secondary phases（AgSnSe2）.At 773 K aMzT～1.33 was achieved in Ag and Na co-doped SnSe possessing Ag8SnSe6secondary phases.The lowκwas credited to the nanoscale precipitate secondary phases（Ag6SnSe8）.The effect of nanostructuring onκlis related to phonon mean free path（MFP）.Luo et al.calculated frequency-dependent phonon MFP using Callaway’s model［98］.Their calculations suggested point defects and Umklapp scattering mostly affect high-frequency phonons，whereas low-frequency phonons were affected by electron-phonon coupling.The calculated MFP due to nanoscale coherent precipitate was somewhat longer than that of electron-phonon coupling but shorter than those of the point defects and the Umklapp scattering，signifying that nanoprecipitate scattered generally the low-to-middle frequency（long wavelength）phonons.Zhao and coworkers reported a highMzTof～1.5 at 793 K through Ag and Ge co-doping［99］.AMzT～1.2 at 773 K was achieved by suppressingκlvia introducing PbSe secondary phases in the SnSe matrix［97，100］.Besides，SnTe and ZnSe secondary phases have been used to suppress theκlin SnSe polycrystals［101－102］.

In 2004，Kanatzidis and his research team successfully introduced AgSbTe2nanodots into PbTe［103］.They achieved a highMzTdue to the lowκvia enhancing the phonons scattering.Two years later，Biswas and co-workers achieved a peakMzT～2.2 in PbTe endotaxially nanostructured with SrTe as shown in Fig.5（c）［45］.AzTof～2.3 was reported in Na-doped（PbTe）0.8（PbS）0.2［104－105］.This highMzTwas credited to the very lowκlarising from coherent precipitate with interfacial dislocations depicting in Fig.5（d）.The binary PbTe-PbS and PbSe-PbS compounds have been extensively studied and advanced to a state of remarkably high TE performance［106－109］.Besides，the performance of pseudo-ternary Pb（TeSeS）was investigated［42，104，110］.This ternary system has shown highMzTover a wideranging temperature.Also，aMzT～1.2 at 423 K was achieved in TAGS（AgSbTe2mixed with SiGe compounds）.Zhang and co-workers prepared composites in situ with Sb2Te or Ag2Te embedded in the AgSbTe2matrix and obtained aMzTvalue of～1.53［111］.They ascribed this highMzTto the reducedκresultant from nanodomain boundaries phonon scattering.A highMzTof～1.59 at 573 K was obtained in AgSbTe2ternary alloy［112］.This ternary alloy was produced by MA and SPS techniques.The highMzTvalue has been accredited to the largeαat room temperature and extremely low value ofκ.ThisMzTvalue was further enhanced to～1.65.Du et al.introduced nanoscale pores（5－10 nm）to the bulk AgSbTe2shown in Fig.5（e），which were in situ created throughout a melt-spinning SPS synthesis process［113］.

Fig.5 （a）FFT image of the Bi0.5 Sb1.5 Te3 sample.Inset shows nanoscale dislocations（Reproduced with permission［95］，Copyright ? 2015，Science）；（b）HAADF-STEM image of the 0.7 at% Ag-doped Sn0.985 S0.25 Se0.75，depicting spherical nanoscale-precipitate in the matrix，reveals continuous lattice between matrix and precipitate（Reproduced with permission［63］，Copyright ? 2020，Elsevier）；（c）High-magnification image of the PbTe-SrTe lattice.Inset shows a coherent interface between the nanoprecipitate and matrix（Reproduced with permission［45］，Copyright ?2012，Springer Nature）；（d）HRTEM image，display PbS/PbTe coherent interface with interfacial dislocation（Reproduced with permission［104］，Copyright ? 2015，John Wiley and Sons）；（e）High-magnification FESEM image of the AgSbTe2 bulk，and depicting nanopores inside the grains（Reproduced with permission［113］，Copyright? 2011，Springer）；（f）Improved peak MzT values of the nanostructured bulk materials

CoSb3-based TE materials are up-and-coming applicants for power generation applications in the medium temperature range.The same material system can realize high performance forn-type andp-type materials.The cage-like open structure can be found in these materials.Up on filling these cages with the foreign atoms，the phonons scattering can be enhanced.At 800 K aMzT～1.43 was attained in the In0.2Ce0.5Co4Sb12bulk sample［114］.The enhancement inMzTwas attributed to the reducedκresulting from in situ InSb nanoislands phonons scattering.AMzTof～1.5 at 850 K was realized in（GaSb）0.2-Yb0.26Co4Sb12nanocomposite possessing GaSb nanoinclusions［115］.The reducedκwas accredited to the GaSb nanoinclusions，which intensified phonons scattering.The research on the single-filled skutterudites was gradually developed into a multiple-filled skutterudites system so as to further reduceκl.It was shown both experimentally and theoretically that filling the cage with multiple guest atoms is more effective to reduceκl.For example，theMzTvalue of～1.0 for the single-filled CoSb3-based material was enhanced to～2.0 using multiple atoms filling.Shi et al.synthesized CoSb3using Ba，La and Yb cofillers［116］.They obtained a very highMzT～1.7 at 850 K，which was attributed to the enhancedα2σalong with reducedκl.Dissimilar rattling frequencies of the manifold guest’s atomic filling in the cages of CoSb3resulted in the strong scattering of nearly all wavelength phonons，makingκlnear to the theoretical minimum.Magnesium silicide（Mg2Si）and its solid solutions have been explored by Nicolaou in 1976［17］.Also，these materials are promising in the medium range of temperature.AMzT～1.2 at 750 K was realized for Mg2.16（Si0.3Sn0.7）0.98Sb0.02［117］.κlwas reduced due to Mg2Sn-rich nanoscale precipitates distributed in the matrix.Bellanger and the research group produced bulk nanostructured Mg2Si0.4Sn0.6materials composed of nanograins with sizes below 200 nm and excellently dispersed Sn-rich nanoparticles［118］.All the samples were prepared by MA and SPS.It was suggested that the most effective way to suppressκis to synthesize samples with nanoscale grain sizes instead of nanoparticles.Consequently，an ultra-lowκof less than 1.2 W/（m·K）was realized at～300 K in samples with nanoscale grain sizes.A very highMzTvalue of～1.7 at 673 K was achieved in Bi and Cr codoped Mg2Si0.3Sn0.7［119］.Elemental Cr and Sn-rich nanoprecipitates embedded in the matrix were observed.The Cr-containing sample showed a 15%reduction inκlcompared with the only Bi-doped sample while retaining comparable values ofα2σ.Fig.5（f）shows the improvedMzTvalues via nanostructuring in bulks materials.

The preferred strategy to realize developments in thermoelectric is the recent example of phonon-liquid electron-crystal（PLEC）.κlcan be reduced even underneath glasses as phonon scattering becomes stronger by the liquid-like fluctuating sublattice［120－121］.Superionic conductors have been developed as a class of favorable applicants to obtain very lowκbecause these materials show long-range liquid-like ionic performance［122－124］.Cu3SbSe3shows distinctive liquid-like sublattice and has risen as a low-cost promising candidate with intrinsic ultralowκ.Wang and co-workers experimentally measured the temperature-dependent Raman spectra combined with a theoretical approach on Cu3SbSe3and Cu3SbSe4bulks and clarified their different phonon manners［125］.As Cu3SbSe4validates a classicalκ，whereas Cu3SbSe3exhibits a liquid-likeκof～0.7－1.0 W/（m·K）at room temperature［126］.Therefore，these compounds offer an exceptional prospect to vigorously analyze the thermal structure and phonon scattering evolution from definite solid vibration to continuous superionic diffusion.The results revealed the activation of superionic conversion for both structurally inequivalent Cu atoms in Cu3SbSe3，which resulted in a mutual broadband phonon scattering.Also，the results showed that phonon quasiparticles were intensely scattered across the superionic transition besides the diffusion channels，whereas the liquid-like diffusion of Cu was excessively sluggish to entirely downfall the transmission of all transverse phonon modes of Cu3SbSe3.

3 Summary

In the present review，we have discussed in detail the improvement in the thermoelectric figure of merit（MzT）of the thermoelectric materials at bulk（3D）and nanoscale（1D and 2D）.Reducing the thermal transport properties of thermoelectric materials，particularly the lattice part（κl），is a crucial zone that can enable largerMzT.Point-defect engineering and nanostructuring are the two typical approaches to suppress the lattice thermal conductivity.To decouple the interrelated lattice thermal conductivity and mobility，it is suggested to dope/alloy the pure compounds with nearly similar atomic size but different atomic mass dopants.Another effective point defects approach is introducing intentional vacancies in the pure compounds.The lattice thermal conductivity and power factor can be simultaneously optimized due to enhancing phonon scattering and increasing carrier concentration，respectively.Careful tailoring of nanostructures，including dimension，shape and interface，is an effective way to boost the thermoelectric performance.Fabrications of 1D-nanostructure，2D-nanostructure and 3D-nanostructure materials made it possible to suppress the thermal conductivity and increase the Seebeck coefficient due to enhancing phonons scattering at the interfaces and quantum confinement effect，respectively.